Just another update

Task/Ordered-Partitions/REXX/ordered-partitions.rexx

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+/*REXX program displays ordered partitions: orderedPartitions(i,j,k,···)*/
+call orderedPartitions 2,0,2           /*Note:    2,,2    will also work*/
+call orderedPartitions 1,1,1
+call orderedPartitions 1,2,0,1         /*Note:    1,2,1   will also work*/
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────ORDEREDPARTITIONS subroutine────────*/
+orderedPartitions: procedure; #=arg(); hdr=;  bot.=;  top.=;  low=;  high=
+d=123456789                            /*handy-dandy literal for digits.*/
+t=0                                    /*T: is the sum of all arguments.*/
+      do i=1  for #;  t=t+('0'arg(i))  /*sum all the highest #s in parts*/
+      end   /*i*/
+                                       /* [↓]  process each of arguments*/
+  do j=1  for #;   _=arg(j)            /*  _:  is the    Jth   argument.*/
+  len.j=max(1,_)                       /*LEN:  length of args, 0=special*/
+  bot.j=left(d,_);          if _==0 then bot.j=0 /*define the bottom num*/
+  top.j=right(left(d,t),_); if _==0 then top.j=0 /*  "     "    top   " */
+  @.j=left(d,t);            if _==0 then @.j=0   /*define VERIFY digits.*/
+  hdr=hdr _                                      /*build display header.*/
+  low=low || bot.j;         high=high || top.j   /*low and high of loop.*/
+  end   /*j*/
+
+okD=left(0||d,t+1)                     /*define legal digits to be used.*/
+say center(' partitions for: ' hdr" ",50,'─');  say
+
+    do g=low  to high                  /* [↑]   generate ordered parts. */
+    if verify(g,okD)\==0  then iterate /*filter out the unwanted digits.*/
+    p=1                                /*P:  is the position of a digit.*/
+    $=                                 /*$:  will be the transformed #s.*/
+       do k=1  for #                   /*verify the partitions numbers. */
+                                       /*validate#: dups/ordered/repeats*/
+       _=substr(g,p,len.k)             /*ordered part num. to be tested.*/
+       if verify(_,@.k)\==0  then iterate g        /*is digit ¬ valid ? */
+       !=                                          /* [↓]  validate num.*/
+       if @.k\==0  then do j=1  for length(_);     z=substr(_,j,1)
+                        if pos(z,$)\==0            then iterate g /*prev*/
+                        !=!','z
+                        if j==1  then iterate
+                        if z<=substr(_,j-1,1)      then iterate g /*ord.*/
+                        if pos(z,_,1+pos(z,_))\==0 then iterate g /*dup.*/
+                        end   /*j*/
+       p=p+len.k                                      /*point to next #.*/
+       $=$ ' {'strip(translate(!,,0),,',')"}"         /*dress the # up. */
+       end   /*k*/
+
+    say $
+    end      /*g*/
+say
+return